On the Variational Distance of Two Trees

On the Variational Distance of Two Trees

A widely studied model for generating sequences is to "evolve" them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally "far apart" in terms of variational distance.

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Veröffentlicht in:The Annals of applied probability 2006-08, Vol.16 (3), p.1563-1575
Hauptverfasser: Steel, M. A., Székely, L. A.
Format: Artikel
Sprache:eng
Schlagworte:
05C05
05C80
05C90
62P10
92D15
Cavender–Farris–Neyman model
Jukes–Cantor model
Leaves
Markov processes
Molecular biology
Phylogenetics
Phylogeny
phylogeny reconstruction
Probability distributions
q-state Potts model
sequence evolution
Steels
symmetric binary channel
Transition probabilities
tree-based Markov process
Trees
variational distance
Vertices
Yule–Harding distribution
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Beschreibung
Zusammenfassung:A widely studied model for generating sequences is to "evolve" them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally "far apart" in terms of variational distance.
ISSN:1050-5164
2168-8737
DOI:10.1214/105051606000000196